Latest TCS Aptitude Question SOLUTION: what is the remainder when 1212121...(300 times)is divided by99?

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what is the remainder when 1212121...(300 times)is divided by99?

Asked In TCS (11 years ago)

Unsolved Read Solution (10)

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RAKESH  (11 years ago)

12/99 gives rem=12
1212/99 rem=12*2
121212/99 rem=12*3
similarly
12...(8 times 12)/99 rem=12*8
12...(9 times 12)/99 rem=(12*9)/99=9
12...(10 times 12)/99 rem=(12*10)/99=21
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1212121...(300 times)=12...(150 times) gives remainder =(12*150)/99
or 1800/99 gives a remainder 18
ANS 18

Is this solution Helpfull? Yes (41) | No (3)  

Mahesh  (11 years ago)

The concept of 99 is similar to 9, for 9, add all the digits and then divide by 9.
789 divided by 9 gives a remainder of 7+8+9 = 24= 2+4=6

For 99, we ahve to take two digits at a time instead of one digit, which is the case with 9. For 999, it will be three digits at a time.

So, for example if the number is 1212 the remainder is 12+12 = 24

Now in the given number 12 is there for 300 times that is 12+12+ 12..... 300 times, the value is 3600 = 36+00 = 36

The remainder is 36.

Is this solution Helpfull? Yes (7) | No (4)  

Shubhrajit Chowdhury  (11 years ago)

Ans.0
121212121....300 times=(121)...100 times..
Now 99=9*11.
121/11=11
After dividing (121)...100 times with 11 it leaves 1111111.... and remainder 0.
Now 111111111 is divided by 9 and it leaves remainder 0...
So 1212121....(300 times) is compltly divided by 99..
ans.0.

Is this solution Helpfull? Yes (5) | No (9)  

Shubhrajit Chowdhury  (11 years ago)

Ans.2
121212121....300 times=(121)...100 times..
Now 99=9*11.
121/11=11
After dividing (121)...100 times with 11 it leaves 1111111.... and remainder 0.
From here we will get (11)...100 times..or 1111..200times..
Now 111111111 is divided by 9 and it leaves remainder 0..That is 11...9 times.
So by 9 it will be divided 11...upto 198 times..
So for last 11 it will leaves remainder 2..
ans.2.

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saurabh agarwal  (11 years ago)

72 ans.

Is this solution Helpfull? Yes (1) | No (1)  

Vikas dadhich  (11 years ago)

38 bahut mushkil h bhai par kr diya

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harshit malpani  (11 years ago)

1212121/99=12243 and remainder is 63.
63*300=18900
18900/99= 19 and remainder is 90

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shubham agrawal  (10 years ago)

We can write 99 as 3*11*3
Now first devide by 3 we get 444444.....300 times.now we devide by 11 we get 44444...150 times.now again we devide by 3 then we see
For 444 remainder is 0 so for 150 terms of 4 remainder will= 0 ans.

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ARUMALLA DHEERAJ  (9 years ago)

divisibility rule of 99 is same as 9
so add all digits i.e., (1+2)*300=900
hence on dividing above number with 99 give remainder as 1

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Khushboo yadav  (6 years ago)

12121212.......300 times
(1+1+1+1+.......300times)+(2+2+2+2+......300times)
=300+2 (300)=900/99=9ans

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